which governs various physical phenomena, for instance binary mixtures of Bose-Einstein condensates, or the propagation of mutually incoherent wave packets in nonlinear optics, see [1]}, [2]}.
Recently, normalized solutions to system (REF ) have attracted much attention of researchers e.g. [3]}, [4]}, [5]}, [6]}. Bartsch, Jeanjean, Soave [3]} and Bartsch, Soave [4]} dealt with \(\beta > 0\)  and \(\beta < 0\)  respectively, they found solutions to (REF )-(REF ) for specific range of \(\beta \)  depending on \(a_1, a_2\) . In addition, Bartsch, Zhong and Zou [6]} studied (REF )-(REF ) for \(\beta > 0\)  belonging to much better ranges independent of the masses \(a_1\)  and \(a_2\) , they adopted a new approach based on bifurcation theory and the continuation method. Bartsch and Soave [5]} proved the existence of infinitely many normalized solutions to (REF ) with \(\mu _{1}=\mu _{2}>0\)  and \(\beta \le -\mu _{1}\)  by using a suitable minimax argument. For normalized solutions of nonlinear elliptic systems with more general nonlinearities, we refer the reader to [11]}, [12]}, [13]}, [14]}.
